"Recharge indicator light blinks
If the orange recharge indicator light blinks while the system is plugged in and charging, then it is likely that the battery is not installed properly. Click here for instructions on how to properly insert a Nintendo DSi battery.
If you have ensured that the battery is installed properly but the orange light still blinks, check to make sure that the battery is a licensed by Nintendo. The only licensed Nintendo DSi battery will have the model number TWL-003 and will display Nintendo's logo.
If the battery does not have the model number TWL-003 then it is likely not a licensed battery. To purchase a replacement licensed battery, click here.
If you determined that the battery is a licensed version, please call 1-800-255-3700 so that we may assist you further."
basically either your battery is bad or its not inserted properly.
I see. well from what i found digging through google is that it may be a burned fuse. i would say try searching for a way to fix it yourself or for someone with knowledge of the inner working of the dsi to do it.
Also may want to see what more experienced members have to say.